The image above, and the three that follow, are trademarks of various international Woolworth companies. The graphic above represents the Woolworths Group (UK and Ireland). This chain's "three & sixes" -type stores were similar to an American 5 & 10. The UK and Ireland Woolworths division went out of business in 2009.
Graphic from www.woolworths.co.uk  

Deutsche Woolworth GmbH & Company (Germany and Austria) is  variety store chain, which is still in operation. It was a subsidiary of the American parent company until 1998.
Graphic from www.woolworth.de   

Woolworths Group (Australia) is a supermarket-centered company with a "Big W" discount retail division. The Oz-based Woolworths was never affiliated with the American Woolworth operation.
Graphic from www.woolworths.com.au

Woolworths Holdings, Limited (South Africa) operates retail stores and supermarkets and was, also, never a subsidiary of the American company.

Graphic from www.woolworths.co.za